JEFFERSON COLLEGE COURSE SYLLABUS MTH201 CALCULUS III 5 Semester Credit Hours Prepared by: Linda Cook Revised Date: December 14, 2006 by Mulavana J Johny Arts & Science Education Dr. Mindy Selsor, Dean
MTH201 CALCULUS III I. CATALOGUE DESCRIPTION Prerequisite: MTH 185 with a grade of C or better. 5 semester hours credit Calculus III is a continuation of Calculus II. The student will study vectors in two and three dimensions and calculus of several variables. (F, S) II. GENERAL COURSE OBJECTIVES Upon completion of this course the student should be able to: 1. To find the horizontal and vertical components of a force and use it in certain problems in Statics 2. Find the dot product of two vectors and use it to find the angle between two vectors, the scalar and vector projections of one vector onto another and the work done by a force. 3. Find the cross product of two vectors and use it to find the area of a parallelogram and the vector moment due to a force. 4. Find the scalar triple product and vector triple product of three vectors 5. Find parametric and symmetric equations for the line passing through two points. 6. Find an equation of the plane through a given point with a specified normal vector. 7. Find the arc length of a curve defined by a vector function. 8. Find the curvature of a curve. 9. Find the velocity, acceleration, and speed of a particle with a given position function. 10. Given a function of x and y, find all first and second partial derivatives. 11. Find an equation of the tangent plane to a given surface at a specified point on the surface. 12. Find the maximum and minimum values of a function of two variable.
13. Find the directional derivative of a function at a given point in the direction of a given vector. 14. Calculate an iterated integral. 15. Evaluate a double integral. 16. Evaluate a triple integral. 17. Find the area of a region, surface area of a surface and the volume of a solid by using integration. 18. Use cylindrical coordinates to evaluate a triple integral. 19. Evaluate a line integral and use it to find the work done by a force. 20. Find a potential function for a conservative vector field and use it to evaluate a line integral along a given curve. 21. Find the curl and the divergence of a vector field. 22. Evaluate a surface integral and use it to find the electrical and magnetic flux. 23. Use Green s theorem to evaluate a line integral. 24. Use Stokes Theorem to evaluate a line integral. 25. Use the Divergence Theorem to calculate a surface integral. 26. Apply the divergence theorem to evaluate the flux. These objectives will be assessed on the final examination. III. COURSE OUTLINE A. Vectors and the Geometry of Space B. Vector Functions C. Multiple Integrals D. Vector Calculus
IV. UNIT OUTLINE A. Vectors and the Geometry of Space 1. Three- Dimensional Coordinate Systems 2. Vectors 3. The Dot Product 4. The Cross Product 5. Equations of Lines and Planes 6. Cylinders and Quadric Surfaces 7. Cylindrical and Spherical Coordinates B. Vector Functions 1. Vector Functions and Space Curves 2. Derivatives and Integrals of Vector Functions 3. Arc Length and Curvature 4. Motion in Space: Velocity and Acceleration C. Partial Derivatives 1. Functions of Several Variables 2. Limits and Continuity 3. Partial Derivatives 4. Tangent Planes and Linear Approximations 5. The Chain Rule 6. Directional Derivatives and the Gradient Vector 7. Maximum and Minimum Values D. Multiple Integrals 1. Double Integrals over Rectangles 2. Iterated Integrals 3. Double Integrals over General Regions 4. Double Integrals in Polar Coordinates 5. Applications of Double Integrals 6. Surface Area 7. Triple Integrals 8. Triple Integrals in Cylindrical and Spherical Coordinates E. Vector Calculus 1. Vector Fields 2. Line Integrals 3. The Fundamental Theorem for Line Integrals 4. Curl and Divergence 5. Parametric Surfaces and Their Areas 6. Surface Integrals 7. Green s Theorem 8. Stoke s Theorem
9. The Divergence Theorem V. METHOD OF INSTRUCTION A. Lectures B. Class Discussion C. Textbook VI. REQUIRED TEXTBOOK(S) WITH PUBLICATION INFORMATION James Stewart, Calculus, Brooks/Cole, 5 th edition VII. REQUIRED MATERIALS (STUDENT) Scientific or Graphics Calculator. VIII. SUPPLEMENTAL REFERENCES Maple 10 IX. METHOD OF EVALUATION (STUDENT) A. Tests B. Homework Assignment C. Projects D. Final Exam